Converting units and currency

Question

A supermarket in Japan sells soy milk for 398 yen per liter. If there are 83.35 yen per dollar, then what is the price in dollars per quart? Conversions that were given. Dollars per foreign =0.0120 Foreign per dollar 83.35 1 liter= 1.05669

My answer was $5.05 per quart but apparently was wrong.

It often helps to keep the units with you in your calculations. Here $398 Y/L=398\times(Y/D)\times(Q/L)D/Q=\dots$ with obvious abbreviations. — Joonas Ilmavirta, Oct 06 '14 at 18:29
To extend my previous comment, you know that $Y/D=1/83.35$ (since $1D=83.35Y$) and you also know the number $Q/L$. Plug the numbers into the formula and see for yourself. — Joonas Ilmavirta, Oct 06 '14 at 18:50
Sorry if I'm slow math isn't my forte but thanks for the help anyway! — ttone, Oct 06 '14 at 19:07

score 0 · Answer 1 · answered Oct 06 '14 at 18:50

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1 Liter costs $\frac{398 \ \text{Yen}}{\text{liter}} \cdot \frac{ \ \text{Dollars}}{83.35 \ \text{Yen}}$ The result is in Dollars per liter.

Now you have to convert the liters in quart. 1 quart = 0.946352946 Liters

1 Liter$= \frac{1}{0.946352946}$ quarts.

Thus 1 quart costs in Dollar: $\frac{398 \ \text{Yen}}{\frac{1}{0.946352946} \text{quart}} \cdot \frac{ \ \text{Dollars}}{83.35 \ \text{Yen}}$

answered Oct 06 '14 at 18:50

callculus42

30,550

Thank you very much for helping me set it up – ttone Oct 06 '14 at 19:05
You are welcome. I have more or less the same result. I have $\approx 4.52 \ \text{Dollars/quart}$ – callculus42 Oct 06 '14 at 19:08

score 0 · Accepted Answer · answered Oct 06 '14 at 19:01

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$$\frac{398 \text{ yen}}{1 \text{L milk}} \cdot \frac{\text{1 dollar}}{83.35 \text{yen}} \cdot \frac{\text{1 L}}{1.05669 \text{ quarts}} = \frac{398}{83.35 \cdot 1.05669} \frac{\text{dollars}}{\text{quart of milk}} = \\4.518870237\dots \frac{\text{dollars}}{\text{quart of milk}}$$

answered Oct 06 '14 at 19:01

NovaDenizen

4,216
15
23

Thank you very much for verifying the answer – ttone Oct 06 '14 at 19:05

Converting units and currency

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